Methods and apparatus for calibration and temperature compensation of oscillators having mechanical resonators

ABSTRACT

Methods and apparatus for calibration and temperature compensation of oscillators having mechanical resonators are described. The method(s) may involve measuring the frequency of the oscillator at multiple discrete temperatures and adjusting compensation circuitry of the oscillator at the various temperatures. The compensation circuitry may include multiple programmable elements which may independently adjust the frequency behavior of the oscillator at a respective temperature. Thus, adjustment of the frequency behavior of the oscillator at one temperature may not alter the frequency behavior at a second temperature.

RELATED APPLICATIONS

The present application claims the benefit under 35 U.S.C. §119(e) ofU.S. Provisional Patent Application No. 61/363,759, filed on Jul. 13,2010 under Attorney Docket No. G0766.70021US00, and entitled “Methodsand Apparatus for Calibration and Temperature Compensation ofOscillators Having Mechanical Resonators”, which is hereby incorporatedherein by reference in its entirety.

BACKGROUND

1. Field

The technology described herein relates to temperature calibration andtemperature compensation of oscillators having mechanical resonators.

2. Related Art

Oscillators are ubiquitous components in electronic equipment includingwireless and wireline communications systems, entertainment electronics,aerospace systems, and timing systems. The oscillators traditionally areused to provide a reference signal or clock signal, such that precisionof the signal frequency is important. Conventionally, crystaloscillators having quartz crystals as the resonating element have servedas the oscillators of choice because they can be manufactured to provideprecise signal frequencies within ±1.5 parts-per-million (ppm) of atarget frequency value, frequency stabilities of ±2.5 ppm over theentire operating temperature range from −40° C. to +85° C., tunabilityof up to ±15 ppm, aging of below ±1 ppm/year (at 25° C.), typical phasenoise of −138 dBc/Hz at 1 kHz, and power consumption as low as 1.5 mA.

Different categories of crystal oscillators have developed, includingcrystal oscillators (XO), temperature compensated crystal oscillators(TCXO), and oven-controlled crystal oscillators (OCXO). The TCXO is verysimilar to the XO, except that the compensation uses a temperaturesensor and a tuning circuit that allows the frequency of the quartzcrystal resonator to be corrected depending on the temperature. As aresult the temperature stability of a typical XO of about ±10 ppm can bereduced down to ±1.5 ppm or even ±0.5 ppm.

SUMMARY

According to a first aspect, a method of calibrating temperaturecompensation circuitry of an oscillator is provided, the oscillatorcomprising a mechanical resonator coupled to the temperaturecompensation circuitry. The method comprises setting a first temperatureof the oscillator and adjusting a first component of the temperaturecompensation circuitry to set an output frequency of the oscillator to adesired value at the first temperature. The method further comprisessetting a second temperature of the oscillator and adjusting a secondcomponent of the temperature compensation circuitry to set the outputfrequency of the oscillator to the desired value at the secondtemperature.

According to another aspect, a temperature compensation circuitconfigured to form part of an oscillator comprising a mechanicalresonator is provided. The temperature compensation circuit comprises atleast first and second adjustable circuit components configured toindependently alter an output frequency of the oscillator.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and embodiments of the technology will be described withreference to the following figures. It should be appreciated that thefigures are not necessarily drawn to scale. Items appearing in multipleof the figures are indicated by the same or similar reference number inall the figures in which they appear.

FIG. 1 is a block diagram of an oscillator using a mechanical resonator.

FIG. 2 is a graph of the relative frequency error of an oscillator usingan AT-cut quartz crystal.

FIG. 3 illustrates the effect of cut-angle inaccuracy on the relativefrequency error of an oscillator using an AT-cut quartz crystal.

FIG. 4 is a block diagram of an oscillator with temperaturecompensation.

FIG. 5A illustrates the relative frequency error of an oscillator usingan AT-cut quartz crystal and the required tuning signal.

FIG. 5B illustrate the first, second and third order contributions ofthe tuning signal for an oscillator using an AT-cut quartz crystal.

FIG. 6A illustrates a thermistor based network for temperaturecompensation according to the prior art.

FIG. 6B illustrates the output signal of the prior art thermistor basednetwork of FIG. 6A.

FIG. 7A illustrates tuning signal contributions associated with usingone linear and two non-linear circuit elements.

FIG. 7B is a comparison of required and generated tuning signals usingthe composite tuning method according to the prior art.

FIG. 7C illustrates the relative frequency error of the composite tuningnetwork of the prior art resulting from use of the tuning signal of FIG.7B.

FIG. 8 is a flow chart of a calibration procedure for prior artoscillators using mechanical resonators.

FIG. 9 is a flow chart of a calibration procedure for oscillators usingmechanical resonators according to one embodiment.

FIG. 10 is a block diagram of a temperature compensation circuit usingpolynomial parameters according to one embodiment.

FIG. 11A illustrates the relative frequency error residual after a firststep of a polynomial temperature calibration scheme applied to anoscillator using an AT-cut quartz resonator.

FIG. 11B illustrates the relative frequency error residual after asecond step of the polynomial temperature calibration scheme applied toan oscillator using an AT-cut quartz resonator.

FIG. 11C illustrates the relative frequency error residual after a thirdstep of the polynomial temperature calibration scheme applied to anoscillator using an AT-cut quartz resonator.

FIG. 12 illustrates the relative frequency error residual for multiplecut-angle inaccuracies of an oscillator using an AT-cut quartzresonator.

FIG. 13A illustrates the relative frequency error of a Lamb waveresonator on a composite silicon dioxide and silicon stack.

FIG. 13B illustrates the relative frequency error of a Lamb waveresonator on a composite silicon dioxide and silicon stack with forvarious thicknesses of the silicon layer.

FIG. 14A illustrates the relative frequency error residual after a firststep of a polynomial temperature calibration scheme applied to anoscillator using a Lamb wave resonator on a composite silicon dioxideand silicon stack.

FIG. 14B illustrates the relative frequency error residual after asecond step of the polynomial temperature calibration scheme applied toan oscillator using a Lamb wave resonator on a composite silicon dioxideand silicon stack.

FIG. 14C illustrates the relative frequency error residual after a thirdstep of the polynomial temperature calibration scheme applied to anoscillator using a Lamb wave resonator on a composite silicon dioxideand silicon stack.

FIG. 15A illustrates the relative frequency error residual after a firststep of a polynomial temperature calibration scheme with a linearre-adjust applied to an oscillator using a Lamb wave resonator on acomposite silicon dioxide and silicon stack.

FIG. 15B illustrates the relative frequency error residual after asecond step of the polynomial temperature calibration scheme with linearre-adjust applied to an oscillator using a Lamb wave resonator on acomposite silicon dioxide and silicon stack.

FIG. 16A illustrates the relative frequency error residual after a thirdstep of the polynomial temperature calibration scheme with linearre-adjust applied to an oscillator using a Lamb wave resonator on acomposite silicon dioxide and silicon stack.

FIG. 16B illustrates the relative frequency error residual after afourth step of the polynomial temperature calibration scheme with linearre-adjust applied to an oscillator using a Lamb wave resonator on acomposite silicon dioxide and silicon stack.

FIG. 17 is a block diagram of a temperature compensation circuitaccording to one embodiment.

FIG. 18A illustrates the relative frequency error residual after a firststep of the temperature calibration scheme of FIG. 9 applied to anoscillator using a Lamb wave resonator on a composite silicon dioxideand silicon stack.

FIG. 18B illustrates the relative frequency error residual after asecond step of the temperature calibration scheme of FIG. 9 has beenapplied to an oscillator using a Lamb wave resonator on a compositesilicon dioxide and silicon stack.

FIG. 18C illustrates the relative frequency error residual after a thirdstep of the temperature calibration scheme of FIG. 9 has been applied toan oscillator using a Lamb wave resonator on a composite silicon dioxideand silicon stack.

FIG. 19 is a block diagram of a temperature compensation circuit withadditional sub-zero correction compared to the embodiment of FIG. 17,according to another embodiment.

FIG. 20 illustrates the relative frequency error residual after a fourthstep of the temperature calibration scheme of FIG. 9 with additionalsub-zero correction applied to an oscillator using a Lamb wave resonatoron a composite silicon dioxide and silicon stack, according to anotherembodiment.

DETAILED DESCRIPTION

Aspects of the technology are directed to calibration and temperaturecompensation of oscillators having mechanical resonators. According toone aspect, calibration of oscillator temperature compensation circuitryinvolves setting values of independently programmable components of thetemperature compensation circuitry to cause a desired oscillatorfrequency response at each of only a small number of discretetemperatures (e.g., less than ten, less than five, etc., but at leastthree). Accurate temperature compensation over the entire operatingtemperature range of the oscillator may still be provided, without theneed to perform a temperature sweep or any confirmation temperaturemeasurements.

According to one aspect of the technology, oscillator temperaturecompensation circuitry includes at least three independentlycontrollable/programmable components each configured to set thefrequency response of the oscillator at a respective temperature.Setting each of the components suitably to provide a desired oscillatorfrequency response at a respective temperature may provide accuratetemperature compensation of the oscillator over the entire operatingtemperature range (e.g., from −40° C. to +85° C. or any other suitableoperating temperature range). According to some embodiments, thecontrollable/programmable components are digital-to-analog converters(DACs).

The aspects described above, as well as additional aspects, aredescribed further below. These aspects may be used individually, alltogether, or in any combination of two or more, as the technology is notlimited in this respect.

A basic oscillator using a mechanical resonator is shown in FIG. 1. Itcomprises a closed loop comprising a resonator 102 producing an outputsignal 104 and an amplifier 106 producing a feedback signal 108. Forthis system to operate as an oscillator and sustain steady-stateoscillation it must fulfill the Barkhausen stability criteria, requiringthat the loop gain equal unity and the phase around the loop is aninteger multiple of 360°, including 0°, and negative integers.

In the most simple case the amplifier will have a phase delay equivalentto 0° phase shift and the mechanical resonator will show a phase shiftof 0° at the resonance frequency of the mechanical resonator. As aresult the oscillator will oscillate at the resonance frequency definedby the resonance frequency of the resonator. In some cases an invertingamplifier is used that introduces a phase change of −180°. As a result,a phase shift of ±180° or any odd multiple of 180° has to be added tothe oscillator loop for the oscillator to oscillate at a frequency closeto or identical to the resonance frequency of the resonator.

It should be understood that for a practical oscillator the phase shiftintroduced by the amplifier will range between 0° and as much as ±45°.The resonator might operate at a frequency related to a phase shift thatwill be close to 0°, but might be as much as ±45°. However, theapplicability of the various aspects described herein is not limited bythe amount of phase delay introduced by any of the components of theoscillator.

The resonance frequency of oscillators including mechanical resonatorsis temperature dependent. The resonance frequency of the mechanicalresonator defines the oscillation frequency of the oscillator. Theresonance frequency of any mechanical resonator is a function of theoperating temperature, and in particular the temperature dependence ofthe stiffness coefficients, density, thermal expansion and temperaturerelated induced stresses of components of the mechanical resonator. Asmentioned previously, quartz crystals have been used conventionally asthe resonators of choice in oscillators. The relative frequencydeviation of the resonance frequency for a conventional AT-cut quartzcrystal resonator is shown in FIG. 2. The relative frequency deviationover the entire temperature range illustrated is in this case less than±8 ppm. Although the circuit components of an oscillator mayadditionally contribute to temperature-dependent frequency behavior, itcan be assumed in appropriate circumstances that the dominanttemperature-dependent frequency behavior of an oscillator arises fromthe mechanical resonator. Thus, an oscillator including the mechanicalresonator operating as shown in FIG. 2 will show substantially the sametemperature-dependent behavior.

The frequency response illustrated in FIG. 2 assumes a particular cutangle for the AT-cut quartz crystal. However, altering the cut angle ofthe quartz crystal alters the temperature dependent behavior of thecrystal, and thus the temperature dependent frequency behavior of anoscillator including the quartz crystal. FIG. 3 illustrates alternativefrequency response curves 304 and 306 of a conventional quartz resonatorfor two additional cut angles of the quartz crystal.

The temperature stability of oscillators using quartz AT-cut resonatorsis generally in the range of ±10 ppm over a temperature operating rangefrom −40° C. to +85° C. For many applications this frequency stabilityis not sufficient. Numerous applications require frequency stabilitiesbetter than ±2.5 ppm or even ±0.5 ppm. To achieve better frequencystability of the crystal oscillator (XO), a temperature compensationcircuit is added to the oscillator circuit. A block diagram of such adevice 400 is shown in FIG. 4. The temperature compensation circuit 404receives signal 410 and employs a tuning method that either induces afrequency shift of the resonator or of the circuit, or both. It shouldbe understood that many techniques are feasible. For the compensationcircuit 404 to apply a suitable temperature dependent compensatingsignal 412 it requires information of the exact temperature of theresonator, which it receives from the connected temperature sensor 406.

The achievable temperature accuracy of the temperature compensatedoscillator shown in FIG. 4 depends on how deviations of the mechanicalresonator, the temperature sensor, the compensation circuit, the circuitcomponents of the oscillator, parasitics, and effects regarding thetuning method employed by the compensation circuitry can be controlledor accounted for by the compensation circuit. The compensation circuitcomprises different adjustable parameters to account for thesevariations. The actual adjustment of the compensation circuit isperformed during a calibration sequence. This assumes though that allcontributions are stable with time, i.e. that there is no aging orhysteresis. In reality, there may be variations over time, but that is aseparate issue addressed separately from initial calibration of thetemperature compensation circuitry.

As mentioned previously, conventional oscillators with resonatorsutilize quartz crystals as the resonators. Thus, calibration oftemperature control circuitry has evolved on the basis that quartzcrystals are being used. One solution to compute the temperaturedependent tuning signal for the oscillator is to use a microcontrollerwith memory as the compensation circuit. Referring to plot 500 of FIG.5A, during the calibration the frequency deviation (i.e., temperaturedependent frequency response) 502 of the oscillator is measured bysweeping through the entire operating temperature range and then thetuning values that would be required to produce the complementaryresponse 504 are stored in the memory. Thus, by applying those tuningvalues during operation of the oscillator, the frequency response istemperature compensated. Such oscillators are often referred to asMicrocomputer Compensated Crystal oscillators (MCXO). They have theinherent drawbacks that they require more power, larger die area andcause frequency discontinuities in the oscillator output.

The most popular high stability crystal oscillators use a compensationcircuit and not a microcontroller, due to the miniature size, cost andstability of the compensation circuit. However, it is difficult for acircuit to imitate the temperature dependency of a mechanical resonator.To see this, plot 550 of FIG. 5B separates the frequency response 502 ofFIG. 5A into the various contributions, including first order 552,second order 554 and third order 556 dependencies. These differenttemperature dependencies can be related to the temperature dependenciesof the resonator material, the electrode materials, stress effects,mounting, and the circuit components of the oscillator. As seen, thelinear component 552 is large, as well as the third order component 556.It is difficult for a circuit to reproduce these different contributionsand the resulting characteristics of the frequency response 502.

A conventional circuit 600 used as a temperature compensation circuitfor AT-cut quartz resonators is shown in FIG. 6A. It assumes a supplyvoltage to be applied at the input 602 and the output signal 604,representing a tuning signal, is shown in FIG. 6B (as 652 in plot 650).In this case the compensation circuit is not connected to onetemperature sensor, but rather uses three temperature dependentresistors (606, 608, 610), also referred to as thermistors. Theresistors 607, 609 and 611 are adjusted to compensate the temperaturecharacteristics of AT-cut crystals. The drawbacks of this technology arethat the resistors have to be trimmed and that the output signal is afunction of all resistors to be trimmed, i.e., they do not operateindependently. That means, although resistor 607 mainly influences thetemperature characteristics at very low temperatures it does affect thecharacteristics at room temperature and high temperatures. The resistor609 is mainly for adjusting the characteristics at room temperature, butnevertheless influences the tuning signal significantly at hightemperatures. This means that, after extracting the relative frequencyerror over temperature for a particular resonator, a sophisticatedalgorithm is required to compute a set of resistor values (607, 609,611) for the particular resonator. It also means that errors due to thelimited accuracy of the trimming will affect the temperaturecompensation behavior over the entire temperature range, and as a resultthe oscillator has to be re-measured to verify the compensation circuitsettings.

Another approach found in literature is to separate the tuning signalinto one linear contribution 702 and two highly non-linear signals 704and 706, as shown in plot 700 of FIG. 7A. Using an optimized combinationthereof yields a compensation signal 712, shown in plot 710 of FIG. 7B,that is very close to the optimum tuning signal 504 previouslydescribed. As a result an oscillator using this tuning method achieves atemperature stability illustrated in plot 720 of FIG. 7C as line 722. Inthis case the frequency error of initially ±8 ppm has been reduced toabout ±1 ppm. Nevertheless, a residual error exists due to thelimitations of the compensation contributions 702, 704 and 706. Again,as seen previously for the resistive network compensation circuit ofFIG. 6A, the contributions 702, 704 and 706 are not exclusive for aparticular temperature range. For example, at a relative temperature of−20K the tuning signal contains a large contribution from 702, asignificant contribution from 704 and a minor contribution from 706.This means that, for example, adjusting contribution 704 will have asignificant effect on the tuning signal over the entire temperaturerange. This means that the three contributions cannot be adjustedindividually, but instead that all three contributions have to beadjusted as part of an optimizing algorithm after the relative frequencyerror of the oscillator is known over temperature.

In general, the calibration procedure for TCXOs with quartz crystalresonators involves multiple temperature sweeps over the entireoperating temperature range. The process 800 is shown in FIG. 8. Theoscillator fabrication process 802 starts at step 804 with thedefinitions of the oscillator frequency, e.g., 26 MHz, and definition ofthe tolerances, including the initial frequency accuracy of e.g. ±1.5ppm, temperature range, e.g., from −40° C. to +85° C. and correspondingtemperature stability of the frequency of ±2.5 ppm. The quartz crystalresonator is then fabricated 806 and undergoes a trimming process 850 sothat the frequency of the oscillator matches the target frequency of, inthis case, 26 MHz with very high accuracy. The trimming sequenceconsists of the actual trimming step 808, in which material is removedor added to the resonator and a comparison step 810, in which theobtained oscillator frequency is compared to the desired frequency,which might include some specified offset. If the comparison of thesetwo frequencies is acceptable, the process continues, otherwise thetrimming step 808 is repeated and the trimming sequence iterated untilthe part passes or is classified a faulty part.

Next, in step 812 the oscillator is swept over temperature to evaluatethe temperature characteristics. This involves setting the oscillator toa large number (typically around 1,200) of precise temperatures over theanticipated operating temperature range and measuring the oscillatoroutput frequency at each of these temperatures. Then in step 814, basedon the extracted relative frequency error over temperature of theoscillator the temperature compensation circuit is adjusted for thatparticular oscillator. To verify that the oscillator fulfills thespecifications of e.g. ±2.5 ppm over the entire temperature range theoscillator is then measured over the temperature range once more in step816. Step 818 is required to ensure that the adjusted oscillator meetsthe specifications. If the oscillator passes this stage it is complete(820). If it does not pass, the part might be re-adjusted (step 814) andthe measurement procedure 816 repeated or the part classified as faulty.

The existing procedure for obtaining TCXOs shown in FIG. 8 has severaldrawbacks.

First, each oscillator behaves differently so that each oscillator hasto be measured over the entire temperature range and adjustedindividually. Second, the temperature measurements require a very highaccuracy on the temperature control during the measurement. As a result,the temperature slope for the measurement is very low and themeasurement procedure takes a lot of time. Because the temperature sweepis performed twice (i.e., steps 812 and 816), the time is even greater.

One reason for taking very high density frequency measurements overtemperature (i.e., a temperature sweep) is the existence of activitydips, also referred to as Q-dips, particular to quartz resonators. Thisphenomenon relates to a multitude of acoustic modes existing in anygiven quartz resonator structure. Although the main resonance mode isinherently very temperature stable, other unused and undesirable modesnevertheless exist and these modes are not necessarily temperaturecompensated. As a result, unwanted modes with frequencies in thevicinity of the main mode that posses a large temperature coefficient offrequency can, for a given temperature, approach and cross the mainmode. In these cases the energy supplied to the resonator by theoscillator circuit is also supplied and stored in these unwanted modes.Moreover, energy stored in the main mode and the unwanted mode can alsointeract, which is often referred to as coupling. As a result, theoscillator frequency for a temperature at which an unwanted modeapproaches the main mode closely enough might show a sudden increase ordecrease in frequency, referred to as “dip”. The existence of activitydips is very hard to predict, as it depends on the exact resonatorgeometry, crystal cut-angle, electrode geometry and the mounting of theresonator. Thus, to discover and account for such dips, the conventionalcalibration routine of FIG. 8 requires the temperature sweep with alarge number of temperatures.

According to one aspect of the technology described herein, a procedurefor calibrating temperature compensated oscillators, including TCXOs, isprovided that is much faster than conventional methods, and onlyrequires the measurement of the oscillator frequency at a small numberof temperatures, as few as two, three or four temperatures. According toanother aspect, compensation circuits are provided for performing themethod just described, and include independently controllable componentsfor calibrating the compensation circuit at respective temperatures.

A non-limiting example of a procedure for calibrating oscillators havingmechanical resonators according to an aspect of the technology is shownin FIG. 9. The oscillator fabrication process 902 starts with thedefinitions of the oscillator frequency, e.g., 125 MHz, and definitionof the tolerances, including the initial frequency accuracy of e.g.,±2.5 ppm, temperature range, e.g., from −40° C. to +85° C. andcorresponding temperature stability of the frequency of ±2.5 ppm.Additional specifications are possible. The resonator is then fabricated906.

The next step depends on whether an arbitrary frequency oscillator isbeing formed or a non-arbitrary frequency oscillator. As used herein,“arbitrary frequency” refers to a frequency not substantially matching aconventional standard oscillator frequency. For example, the arbitraryfrequency may differ by at least 30 parts per million (ppm) from astandard oscillator frequency in some embodiments. In some embodiments,the arbitrary frequency may differ by at least 50 ppm from a standardoscillator frequency, by at least 100 ppm, by at least 200 ppm, by atleast 500 ppm, by at least 1,000 ppm, or by between approximately 1,000ppm and 10,000 ppm (e.g., 2,000 ppm, 5,000 ppm, or any other valuewithin this range), among other possible amounts of deviation. The term“arbitrary frequency” as used herein does not imply the frequency is notknown or cannot be measured. Rather, an arbitrary frequency may bemeasured or otherwise have its value determined

In some embodiments in which an arbitrary frequency oscillator is beingformed (i.e., an oscillator not required to meet a conventional orstandard oscillator frequency (e.g., 26 MHz)), the oscillator frequencyis measured at a first temperature (step 908), e.g., around roomtemperature with a rather large tolerance on the temperature accuracy,and the frequency of the oscillator recorded at 910 within, for example,memory of the oscillator or a test-computer. In this manner, the initialfrequency of the oscillator may be available for future reference. In analternative embodiment in which an arbitrary frequency oscillator isbeing formed, the step 950 may be omitted since the initial frequencyvalue can be arbitrary, so that step 920 may be performed directly afterstep 906. For those embodiments in which an oscillator of non-arbitraryfrequency is being formed (i.e., an oscillator with a frequency intendedto meet a conventionally accepted oscillator frequency (e.g., 26 MHz)),the illustrated step 950 may be replaced with a trimming step of thetype previously described with respect to step 850.

In step 920 the oscillator is exposed to a well-defined firsttemperature (Temperature 1), which is controlled within an accuracy of±5 K, ±1 K, ±0.5 K or even ±0.1 K, as non-limiting examples. Largervalues are also possible. The oscillator frequency is then measured. Thecompensation circuit within the oscillator is then adjusted (step 922)and the resulting (adjusted) oscillator frequency is compared to thedesired frequency in step 924. The procedure of measuring 920, adjusting922 and comparing 924 is repeated until the oscillator frequency matchesthe desired frequency at the first temperature.

It should be understood that the desired frequency may be any suitablevalue, and that the method illustrated in FIG. 9 is not limited in thisrespect. According to one embodiment, the desired frequency may be thefrequency determined and stored in step 910, or it may be the frequencymeasured in step 920. In such situations, no circuit adjustment may benecessary at 922. In alternative embodiments, the desired frequency maybe computed based on the stored frequency in 910 and the measuredfrequency of step 920. It should also be appreciated that the frequencyused for comparison in step 924 may be the frequency determined andstored in step 910 including a defined offset, may be the frequencymeasured in step 920 with a specified offset, or may be a frequencycomputed based on the stored frequency in 910 and the measured frequencyof step 920 including an offset, among other possibilities.

In step 930 the oscillator is exposed to a well-defined secondtemperature (Temperature 2), which is controlled within an accuracy of±5 K, ±1 K, ±0.5 K or even ±0.1 K, as non-limiting examples. Largervalues are also possible. The oscillator frequency is then measured. Thecompensation circuit within the oscillator is then adjusted (step 932)and the resulting (adjusted) frequency is compared to the desiredfrequency in step 934. The procedure of measuring 930, adjusting 932 andcomparing 934 is repeated until the oscillator frequency matches thedesired frequency. In one embodiment, the desired frequency used forcomparison in 934 is the same as the frequency used for the comparisonin 924. Alternatively, in some embodiments the desired frequency in 934may be chosen to include an offset to the desired frequency used in 924.

In step 940 the oscillator is exposed to a well-defined thirdtemperature (Temperature 3), which is controlled within an accuracy of±5 K, ±1 K, ±0.5 K or even ±0.1 K, as non-limiting examples. Largervalues are also possible. The oscillator frequency is then measured. Thecompensation circuit within the oscillator is then adjusted 942 and theresulting (adjusted) frequency is compared to the desired frequency instep 944. The procedure of measuring 940, adjusting 942 and comparing944 is repeated until the oscillator frequency matches the desiredfrequency (in which case the procedure is completed at 946). In oneembodiment, the desired frequency used for comparison in 944 is the sameas the frequency used for the comparison in 924 and 934. In someembodiments the desired frequency in 944 may be chosen to comprise anoffset to the desired frequency used in 934.

If the oscillator has passed step 944, it is complete. If the oscillatorrepeatedly does not pass the comparison steps 924, 934, or 944 or if thefrequency despite the adjustment is not able to approach the comparisonfrequency, the part is classified as faulty and taken out of theprocedure. It should be further appreciated that the embodiment shown inFIG. 9 containing three temperature points and circuit adjustment stepscan be extended to comprise additional temperatures and circuitadjustment steps, and can contain four, five or even six suchcalibration steps and is not limited in this respect. The greater thenumber of temperatures measured, the greater the accuracy of thecalibration.

The method illustrated in FIG. 9 may be used beneficially foroscillators including various types of mechanical resonators. Forexample, the method may be used beneficially for oscillators havingmicroelectromechanical systems (MEMS) resonators. The method may also beused beneficially for oscillators using quartz resonators, thus avoidingthe temperature sweeps associated with the conventional method of FIG. 8for calibrating such oscillators.

One embodiment of a temperature compensation circuit which may utilizethe calibration procedure 900 is shown in block diagram form in FIG. 10.It comprises a temperature sensor 1002 that outputs a current, voltageor charge dependent on the temperature. Initially, the digital to analogconverters 1024, 1028, 1032 are all set to their smallest value, i.e.,zero.

The calibration of circuit 1000 of FIG. 10 may depend on the type ofresonator being used with the oscillator of which the circuit 1000 is apart. If an AT-cut crystal is used that is trimmed to a specificfrequency the sequence 950 may be replaced with the trimming procedure850. For an arbitrary frequency oscillator, sequence 950 may be used oromitted depending on whether a circuit adjustment is necessary at thefirst step or not, as discussed above. In explaining the calibration ofcircuit 1000, we will assume that the procedure 950 is omitted.

The circuit is initially set to a desired first temperature at step 920,for example by adjusting the circuit temperature until the temperaturesensor 1002 indicates the circuit is at the desired temperature. As anon-limiting example, if the temperature sensor outputs a signalindicative of a difference between the desired temperature and theactual temperature, then the circuit temperature may be adjusted untilthe output of the temperature sensor 1002 is nulled. The frequency ofthe oscillator is then measured at step 920. This first temperature stepcan be chosen arbitrarily, but a temperature close to the center of theexpected operating temperature range of the oscillator is advantageous.Room temperature (25° C.) is a preferred temperature, however, othertemperatures are also possible. At this first temperature step, theelectrical signal at 1010 is measured by measuring the electrical signalat Pin A 1012. The electrical signal 1010 is the sum of the temperaturesensor signal 1004 and a value stored in element 1006 (adigital-to-analog converter (DAC) in this non-limiting embodiment)formed by the adder 1008. The objective is to null the signal 1010. Byadjusting the value of DAC 1006 and measuring the output signal at 1012the signal 1010 is set to zero. As shown, a special pin (e.g., pin 1012)might be available on the oscillator to measure signal 1010. However,other embodiments are possible. For example, signal 1010 may be providedat the oscillator output. In still other embodiments, the measurement of1010 might occur internally and a value relating to the level of signal1010 might be accessible through memory in the oscillator that is alsoaccessible from the outside.

As mentioned, by suitably adjusting the value of 1006, the signal 1010is zero at the first temperature. As a result, the signals 1014 a, 1014b and 1014 c are also zero. Therefore, the output signal of the adder1016 is also zero. The tuning circuit output signal 1022 from adder 1020is therefore determined by the value stored in 1018 (also a DAC in thisnon-limiting embodiment). This value can be either left as is,corresponding to the case where the desired frequency is chosen as thefrequency measured in step 920 and therefore no adjustment is necessaryor the value is adjusted to match a desired frequency based on theoscillator specifications from step 904, the frequency stored in step910, or the value measured in step 920, or a combination of the formerthree, including any arbitrary offset. The value of DAC 1018 can also bechosen to match a certain number of significant digits, e.g., if themeasured frequency in step 920 is, e.g., 124,897,064.26 Hz the desiredfrequency could be chosen to require fewer significant digits, e.g.,124,897,000.00 Hz. No matter how it is chosen, this first frequency thatis used for the adjustment criteria is referred to as the desiredfrequency.

In the next step, the linear coefficient of the temperaturecharacteristics of the oscillator is adjusted. The oscillator is broughtto the second temperature, step 930, and the frequency of the oscillatormeasured. The linear term of the compensation signal, which is producedby mixer 1026 (M1) and is controlled by DAC 1024, is then adjusted atstep 932 by programming 1024 so that the oscillator output (not shown inFIG. 10) is equal to the desired frequency or offset from the desiredfrequency by a specific amount, i.e., until the result passes atcomparison step 934. As a result the oscillator is now compensated tofirst order. The typical temperature dependent frequency response 202 ofan AT-cut quartz crystal is shown in plot 200 of FIG. 2 before linearcompensation. The temperature dependent frequency response 1102 afterthe linear compensation just described is shown in plot 1100 of FIG.11A. The point indicated by 1104 represents the working point (at atemperature represented by the corresponding vertical line) where thefrequency error is minimized by adjusting the circuit as just described.In the various plots shown herein relating to aspects of the presentinvention, the vertical gray lines represent temperatures which may beused in the calibration processes (e.g., Temperature 1, Temperature 2,Temperature 3, etc.).

As seen from FIG. 5B, the frequency response of the AT-cut crystal alsocomprises large second and third order components. To extract the lineartemperature adjustment correctly according to the methodology ofoperation of circuit 1000, a temperature is chosen where the second andthird order coefficients are equal in amplitude, but opposite in sign.For AT-cut crystals, depending on the electrode materials and thickness,this temperature is between 34° C. and 39° C. Thus, this temperaturerange is preferred for adjusting the linear coefficient.

In the third temperature step the quadratic temperature dependence isadjusted. Element 1028 (a DAC in this non-limiting example) is adjustedto yield a quadratic term 1030 that is added by adder 1016 to thealready adjusted linear signal 1014 a. Because the second ordercontribution is larger than the third order coefficient close to thefirst temperature, a third temperature is chosen that lies either inbetween the first and second temperatures or that lies below the firsttemperature but within some range of the first temperature, the rangebeing defined by the difference of the first temperature minus thesecond temperature. Other temperatures for the third temperature arealso possible, especially if the resonator is not an AT-cut crystal.After adjusting the circuit for the third temperature to match thedesired frequency, possibly including an offset, the oscillator passesthe comparison 944 and the resulting temperature dependent frequencyresponse including a first and second order compensation is shown inFIG. 11B. The point indicated by 1114 represents the working point wherethe frequency error is minimized by adjusting the circuit, and thevertical gray lines represent the temperatures used during thecalibration process.

As seen from plot 1110 of FIG. 11B the frequency response 1112 stillcontains a large third order contribution, which may be removed with ameasurement at another temperature in addition to those illustrated inFIG. 9 (i.e., at a “Temperature 4” after the processing at “Temperature3”). While this additional processing at yet another temperature is notillustrated in FIG. 9 for purposes of simplicity of the illustration, itshould be understood that the processing at this additional temperatureis identical to the processing performed at the first, second and thirdtemperatures (i.e., Temperatures 1-3), meaning that the processinginvolves measuring the oscillator frequency at Temperature 4 and thenadjusting the circuit to provide the desired frequency response at thattemperature, and repeating as necessary. At this fourth temperature, thevalue of which is chosen close to extremes of the expected operatingtemperature range of the oscillator, the cubic component 1034 in FIG. 10is adjusted using the DAC 1032 until the desired frequency is reached,possibly including an offset. After passing this comparison the part iscompleted. The frequency response of the fully adjusted oscillator isshown in plot 1120 of FIG. 11C. The point indicated by 1124 representsthe working point where the frequency error is minimized by adjustingthe circuit as just described. As shown, the frequency error of 1112 iswell below the typical temperature stability of AT-cut crystal basedoscillators.

As mentioned, the temperature dependent frequency response of a crystaloscillator may depend on the cut angle of the oscillator. Applying thecalibration procedure just described to AT-cut crystal-based oscillatorsfor the three different cut angles used to generate the frequencyresponse curves of plot 300 in FIG. 3 results in the three correspondingcurves shown in plot 1200 of FIG. 12, where 1202 corresponds to theinitial curve 202 after compensation using the method of FIG. 9, 1204corresponds to 304 after compensation, and 1206 corresponds to 306 aftercompensation. It is apparent that the temperature error is very smallfor the temperature range spanned by the smallest and largestmeasurement temperature. However, for temperatures outside of thetemperature range spanned by the calibration temperatures the error isconsiderable. In this example negative temperatures have been avoided,i.e. the smallest temperature in this example is 22.5° C. To reduce thefrequency error for negative temperatures, several methods can be used.One method expands the temperature test range to include negativetemperatures. Another method is based on using a known offset for thefrequency adjustment to account for the negative temperatures. Anothermethod uses an offset added or subtracted to the temperature sensor.

The foregoing discussion of calibration techniques has been focused onthe context in which an oscillator, prior to compensation, exhibits atemperature dependent frequency response having the shape shown in FIG.2, as is typical for conventional crystal oscillators. However, analterative temperature dependent frequency response is seen for sometypes of Lamb wave resonators using special temperature compensatedstacks. For example, plot 1300 of FIG. 13A illustrates an alternativeshape of a temperature dependent frequency response of an oscillator,shown by the line 1302. A frequency response like that shown in FIG. 13Amay be exhibited by the types of resonators having a temperaturecompensated stack comprising layers of silicon dioxide, silicon, andsilicon dioxide, as described in U.S. patent application Ser. No.12/639,161, filed on December 16, 2009 under Attorney Docket No.G0766.70006US01 and entitled, “Mechanical Resonating StructuresIncluding a Temperature Compensation Structure,” and published as U.S.Patent Application Publication No. US-2010-0182102-A1 on Jul. 22, 2010,which is hereby incorporated herein by reference in its entirety. Inthis case the turnover temperature (i.e., the temperature at which thefrequency response hits a peak value, like that shown in FIG. 13A) isdesigned to lie close to the center of the temperature operating range.As with most materials, silicon has a large negative first ordercoefficient of frequency, a large second order contribution and asignificant third order contribution, related to the stiffnessdependence over temperature and thermal expansion dependence overtemperature. Silicon dioxide possesses the rare characteristic that thestiffness increases with increasing temperature. This rarecharacteristic can be used to create temperature stable resonators bymatching the silicon dioxide thickness to the silicon thickness. As aresult the first order temperature dependence can be accounted for, asshown in FIG. 13A. However, a large second order dependence remains asseen from FIG. 13A, that also includes a significant third ordercontribution that is hard to make out from trace 1302.

As previously described, for an AT-cut crystal the cut angle dependenceof the crystal resonator is one of the biggest factors that influencesthe resulting temperature characteristics, as shown in FIG. 3. For thecase of a composite compensating layer stack (e.g., a composite stackincluding silicon sandwiched between layers of silicon dioxide, asdescribed in the above-incorporated U.S. patent application Ser. No.12/639,161) including one or more compensating material layers, thetemperature characteristics are influenced by the thickness tolerancesin manufacturing the composite stack. The effect of the thicknessvariations for a compensated stack resonator are shown in FIG. 13B. Thecalibration procedure described herein is versatile enough to accountfor these variations of the temperature characteristics originating fromthe thickness variations. It should be appreciated that not only thethickness tolerances affect the temperature characteristics of theresonator, but also the control and repeatability of the resonatorgeometry and the material properties of the materials involved should bewell controlled, including stiffness, intrinsic stress, chemicalcomposition, as well as the temperature profile and related annealingeffects that can influence the material properties during fabrication aswell as during operation.

The results of applying the calibration procedure shown in FIG. 9 to acompensated stack resonator having the pre-calibration frequencyresponse shown in FIG. 13A (e.g., of the type described in theabove-incorporated U.S. patent application Ser. No. 12/639,161) areshown in FIGS. 14A-C. For an arbitrary frequency oscillator the sequence950 may be used or omitted depending on whether a circuit adjustment isnecessary at the first step or not, as discussed above. We will assumehere that the procedure 950 is omitted.

The circuit is initially set to a desired first temperature at step 920,for example by adjusting the circuit temperature until the temperaturesensor 1002 indicates the circuit is at the desired temperature. As anon-limiting example, if the temperature sensor outputs a signalindicative of a difference between the desired temperature and theactual temperature, then the circuit temperature may be adjusted untilthe output of the temperature sensor 1002 is nulled. The frequency ofthe oscillator is then measured at step 920. This first temperature stepcan be chosen arbitrarily, but a temperature close to the center of theexpected operating temperature range of the oscillator is advantageous.Room temperature (25° C.) is a preferred temperature, however, othertemperatures are also possible. At this first temperature step, theelectrical signal at 1010 is measured by measuring the electrical signalat Pin A 1012. The electrical signal 1010 is the sum of the temperaturesensor signal 1004 and a value stored in element 1006 (a DAC in thisnon-limiting embodiment) formed by the adder 1008. The objective is tonull the signal 1010. By adjusting the value of DAC 1006 and measuringthe output signal 1010 the signal 1010 is set to zero. As shown, aspecial pin (e.g., pin 2010) might be available on the oscillator tomeasure signal 1010. However, other embodiments are possible. Forexample, signal 1010 may be provided at the oscillator output. In stillother embodiments, the measurement of 1010 might occur internally and avalue relating to the level of signal 1010 might be accessible throughmemory in the oscillator that is also accessible from the outside.

As mentioned, by suitably adjusting the value of 1006, the signal 1010is zero at the first temperature. As a result, the signals 1014 a, 1014b and 1014 c are also zero. Therefore, the output signal of the adder1016 is also zero. The tuning circuit output signal 1022 is thereforedetermined by the value stored in 1018. This value can be either left asis, corresponding to the case where the desired frequency is chosen asthe frequency measured in step 920 and therefore no adjustment isnecessary or the value is adjusted to match a desired frequency based onthe oscillator specifications from step 904, the frequency stored instep 910, or the value measured in step 920, or a combination of theformer three, including any arbitrary offset. The value of DAC 1018 canalso be chosen to match a certain number of significant digits, e.g., ifthe measured frequency in step 920 is e.g., 124,897,064.26 Hz thedesired frequency could be chosen to require fewer significant digits,e.g., 124,897,000.00 Hz. No matter how it is chosen, this firstfrequency that is used for the adjustment criteria is referred to as thedesired frequency.

In the next step, the linear coefficient of the temperaturecharacteristics of the oscillator is adjusted. The oscillator is broughtto the second temperature, step 930, and the frequency of the oscillatormeasured. The linear term of the compensation signal, which is producedby mixer 1026 (M1) and is controlled by DAC 1024 is then adjusted atstep 932 by programming 1024 so that the oscillator output (not shown inFIG. 10) is equal to the desired frequency or offset from the desiredfrequency by a specific amount, i.e., until the result passes atcomparison step 934. As a result the oscillator is now compensated tofirst order. The typical temperature dependent frequency response ofstack compensated resonators before compensation, 1302, 1354 and 1356are shown in plot 1350 of FIG. 13B. After this first compensation stepthe results shown in plot 1400 of FIG. 14A are obtained, where it ishard to separate the different traces from each other, as indicated by1402. The point indicated by 1404 represents the working point where thefrequency error is minimized by adjusting the circuit as just described.

To ensure the turnover temperature coincides with the center of thetemperature operating range, the second temperature is chosen very closeto the center of the temperature range or the first temperature. Thisdecision is based on the temperature characteristics of the resonator.We had seen that for AT-cut crystals it is advantageous to use atemperature between 34° C. and 39° C. for the extraction of the linearcoefficient. For a resonator that is dominated by linear and quadraticcomponents, as is the case for almost all non-quartz mechanicalresonators, the temperature used for the linear adjustment is chosenclose to the center of the temperature range, i.e. within ±10K, ±20K,although other values are also possible.

In the third temperature step the quadratic temperature dependence isadjusted. Element 1028 is adjusted to yield a quadratic term 1030 thatis added by adder 1016 to the already adjusted linear signal 1014 a.Because the second order contribution is much larger than the thirdorder coefficient for compensated stack resonators the third temperatureis chosen to lie at one extreme of the temperature range. As positivetemperatures are technically easier to obtain the maximum temperature of+85° C. is used in this case. After adjusting the circuit for the thirdtemperature to match the desired frequency, possibly including anoffset, the oscillator passes comparison 944 and the resultingtemperature characteristics including first and second ordercompensation are shown in FIG. 14B. The point indicated by 1418represents the working point where the frequency error is minimized byadjusting the circuit as just described.

As seen from plot 1410 of FIG. 14B the temperature characteristics ofall three traces 1412, 1414 and 1416 still contain a large third ordercontribution. It should be noted that for some oscillator applicationsthe temperature stability obtained after the second order compensationshown in FIG. 14B is satisfactory. It should be noted that the resultingtemperature error after the second order compensation of the compensatedstack resonator shown in FIG. 14B is superior to the error in AT-cutcrystals after the second order compensation shown in FIG. 11B forcomparison.

In the case of the residual frequency error over temperature not beingsufficient, a fourth temperature may be used to reduce the effect of thethird order contribution. Following the procedure described previouslyin connection with FIG. 10 for using a fourth temperature (i.e., a“Temperature 4” not illustrated in FIG. 9 but being used after“Temperature 3” in FIG. 9), the reduction of the third order dependenceis only marginal, as seen from plot 1420 of FIG. 14C, in which 1424corresponds to 1414 of FIG. 14B, 1426 corresponds to 1416 of FIG. 14B,and 1422 corresponds to 1412 of FIG. 14B. If the fourth temperature ischosen in between the second and third temperatures the characteristicsfor positive temperatures are improved at the cost of the frequencyerror for negative temperatures. Therefore, a modification to thecalibration sequence may be made to provide even greater reduction ofthe frequency error.

The modified sequence (modified compared to FIG. 9) uses an adjustmentstep at a first temperature to null the temperature sensor, aspreviously described (e.g., by adjusting the circuit temperature untilthe temperature sensor output is nulled). The next adjustment step atthe second temperature is used to compensate the linear contribution asbefore, leading to the result shown in plot 1500 of FIG. 15A, which isidentical to the frequency response shown in FIG. 14A (i.e., 1502 isidentical to 1402 and 1504 is identical to 1404, although it should benoted that FIGS. 14A and 15A differ in that the graphs illustrate notonly the frequency response but also the temperatures (shown in thevertical gray lines) at which the calibration steps are performed, andFIG. 15A shows a temperature at 15 Kelvin whereas FIG. 14A shows thecorresponding temperature line at between 55 and 60 Kelvin). At thethird temperature the second order contribution is adjusted and theresult is shown in plot 1510 of FIG. 15B, which illustrates an identicalfrequency response to that of FIG. 14B (i.e., 1512 is identical to 1412,1514 is identical to 1414, 1516 is identical to 1416, and 1518 isidentical to 1418), although again the figures differ in that theillustrated test temperatures (shown by the vertical gray lines) differ.According to the modified sequence, at the fourth temperature, which ischosen to lie in between the second and third temperatures, the linearterm controlled by 1024 is re-adjusted. In other words, after initiallyadjusting the DAC 1024 to compensate for the linear contribution earlierin the calibration process, that compensation may be negatively impactedby the subsequent compensation of the second order error. Thus, afterthe compensation at the second and third temperatures is performed, theprocess may involve re-adjusting the DAC 1024 to ensure that the linearterm is compensated by readjusting the DAC value until the oscillatorfrequency at the fourth temperature matches the desired frequency. Thisreadjustment at the fourth temperature results in the traces 1602, 1604and 1606 in plot 1600 of FIG. 16A, where 1608 represent the workingpoint at the fourth temperature. Compensation of the third ordercontribution may then be performed using a fifth temperature, which canbe chosen to be identical with the third temperature, resulting in thebehavior illustrated in plot 1610 of FIG. 16B. Trace 1614 corresponds to1604 of FIG. 16A after using the fifth temperature 1618. Likewise,traces 1612 and 1616 correspond to traces 1602 and 1606, respectively,after compensation at the fifth temperature. By adjusting the value ofthe DAC 1032 at the fifth temperature to meet the desired frequency thethird order contribution may be removed. As a result, the residualfrequency error after passing this calibration sequence is about ±1 ppm,and even smaller in the temperature range spanned by the smallest andlargest temperature used during the calibration (see FIG. 16B). Toreduce the residual error even more, negative temperatures can be usedduring the calibration.

Several features of the temperature compensation circuit block diagram1000 shown in FIG. 10 are worth noting. The first is that a firsttemperature step is required to null the temperature sensor reading. Asa result, adjustment of the circuit at four to five temperatures isnecessary to obtain a third order compensation of the circuit. Secondly,adjusting the circuit components as described at any given temperatureaffects not only the frequency response at that temperature but also atother temperatures, including previously tested temperatures. Thiseffect becomes more severe if non-ideal behavior of the circuitcomponents is included, such that the frequency measurement may belimited to an accuracy of, e.g., 0.1 ppm.

The circuit block diagram 1700 shown in FIG. 17 addresses thecharacteristics of circuit 1000 just described since they may beundesirable in some situations.

The circuit 1700 includes a temperature sensor 1702 producing atemperature sensor signal 1704, which is provided to adder A1 1708.DAC*1 1706 also provides its output signal to adder 1708. The adder 1708outputs signal 1710, which may be measured at Pin A 1712. The outputsignal 1710 is branched into signals 1710 a, 1710 b, and 1710 c, whichare provided to mixer M1 1734, adder A2 1730, and quadratic component1726, respectively. DAC 3 1724 also provides its output to the quadraticcomponent 1726, which produces signal 1728. Adder A2 1730 produces anoutput signal 1732 a which may be measured at Pin B 1732 and which isprovided to mixer M2 1738. DAC 5 1736 also provides its output signal tomixer 1738, the output 1714 b of which is provided to adder 1716. Adder1716 also receives an output signal 1714 a of mixer M1 1734. Asmentioned, mixer 1734 receives 1710 a as one input and also receives theoutput of DAC4 1732 as a second input. Adder 1716 is coupled to adder A41720 to provide its output signal to adder 1720. DAC*2 1718 alsoprovides it output to adder 1720, which then provides output 1722 of thecircuit.

The circuit 1700 does not require a distinct calibration of thetemperature sensor signal 1704 from temperature sensor 1702, and thefrequency error at a given temperature is not affected by subsequentadjustments. In this case, including the sequence of 950 in method 900is of interest as it can help during the first actual tuning step toestimate what the overall frequency error over temperature is for aspecific oscillator. From knowing the frequency of the oscillatoraround, e.g., room temperature and at the first measurement temperature

Temperature 1 (step 920) the overall temperature characteristic can beestimated. This is understood from examining FIG. 13B around roomtemperature and the frequency deviation for a 60K higher temperature.Even if the temperature accuracy of the initial frequency measurement instep 908 is large, as large as ±5° C., ±10° C. or even larger, thetemperature characteristics can be estimated. From this estimate, therequired tuning range can be determined and used to define the desiredfrequency of the oscillator. In general, tuning an oscillator will causethe phase noise of the oscillator to increase, which is undesirable.From being able to estimate the required tuning range, the desiredfrequency can be chosen to fulfill various possible requirements ofinterest. For example, if an optimum of the phase noise is desiredaround a specific temperature, the desired frequency can be chosen tocoincide with the frequency the oscillator would have at thistemperature with a tuning signal of zero. In another case, better phasenoise performance may be desired for positive temperatures than atnegative temperatures, which may be achieved by choosing the desiredfrequency to coincide with the frequency of the oscillator with thetuning signal being zero for a temperature larger than the center of thetemperature range.

That means after initially measuring the frequency at Temperature 0,generally close to room temperature (25° C.) in step 908 and storing thefrequency, the oscillator is exposed to a first well controlledtemperature as part of step 920. There is an advantage of choosing thisfirst temperature at one of the extremes of the temperature range. Apositive temperature is generally more desirable. At this first wellcontrolled temperature of step 920 the temperature signal 1710 (outputby adder 1708) is adjusted to zero by controlling DAC 1706 to cancel thetemperature sensor signal 1704, which is done by measuring theelectrical signal at Pin A 1712. As a result of 1710 being zero thetuning signal 1722 depends on the value stored in DAC 1718. Theoscillator frequency is measured and adjusted to match the desiredfrequency by adjusting the value stored in 1718. The resultingtemperature characteristics are shown in plot 1800 of FIG. 18A, whichcorrespond to the results of FIG. 13B simply shifted to be zero at thepoint indicated by 1808 (i.e., 1802 is a shifted version of 1302, 1804is a shifted version of 1354, and 1806 is a shifted version of 1356).

The oscillator is then exposed to the second temperature and thefrequency measured in step 930. This temperature is chosen closer to themost negative extreme of the temperature range. In some cases it mightbe desirable to use a temperature around 0° C. or +5° C., or above −20°C. to avoid technical difficulties of the temperature control and icingrelated reliability issues. The circuit is then adjusted at step 932 bymeasuring the electrical signal 1732 a at Pin B 1732 and adjusting DAC1724 until the electrical signal 1732 a is zero. Then DAC4 1732 isadjusted until the oscillator frequency matches the desired frequency.The resulting frequency error over temperature is shown in plot 1810 ofFIG. 18B, in which 1812 represents the frequency error and 1814represents the working point of the second temperature.

As the third temperature measurement 940 a temperature in between thefirst and second temperatures is chosen. The value of DAC 1736 isadjusted until the oscillator frequency matches the desired frequency.The resulting frequency error is shown in plot 1820 of FIG. 18C, withtraces 1822, 1824, and 1826. Point 1828 represents the working point atthe third temperature. It should be appreciated that for all traces1822, 1824 and 1826 the frequency error at the three measurementtemperatures is zero. The residual frequency error is mostly below ±0.5ppm, however it exceeds this range for the negative temperature range.By choosing the second temperature to be more negative this frequencyerror for negative temperatures can be improved.

A slight modification of the block diagram of circuit 1700 is shown inFIG. 19 as circuit 1900. Those elements that are the same are labeledwith the same reference numbers and so are not described in detail againhere. Circuit 1900 includes additional components such as diode 1940,DAC6 1942, and mixer M3 1944. The signal 1732 a output by adder A2 1730(which may be measured with Pin B 1932) is branched to signal 1732 b andprovided to the diode 1940. The diode 1940 compares the value of signal1732 b to zero and passes the signal only if it is greater than zero.Any suitable circuit component for performing such a function may beused, as a diode is a non-limiting example. The output of diode 1940 isinput to mixer M3 1944, which also receives an output of DAC6 1942.Mixer 1944 then output signal 1714 c to adder 1916. Adder 1916 issimilar to adder 1716 of FIG. 17, except that it receives the additionalinput 1714 c where adder 1716 does not. The output of adder 1916 isprovided to adder A4 1720, as is the output of DAC*2 1718. Adder 1720then provides the output signal 1922 of the circuit.

Circuit 1900 contains the element DAC6 1942 that can be adjusted eitherat a fourth temperature by matching the oscillator frequency to thedesired frequency or 1942 might be set to a value based on the valuesused for 1724 and DAC4 1732. In this case the non-linearity of thedigital to analog converter can have an effect on the accuracy of thetuning signal.

Using circuit 1900, the result shown in FIG. 18C is improved fornegative temperatures, as shown in plot 2000 of FIG. 20. In plot 2000,trace 2002 corresponds to trace 1822 of FIG. 18C improved for negativetemperature, trace 2004 corresponds to trace 1824 improved for negativetemperatures, and trace 2006 corresponds to trace 1826 improved fornegative temperatures. In this case the adjustment was done based on thevalues used for 1724 and DAC4 1732.

While various embodiments described herein have been described as usingat least three temperatures (e.g., the method of FIG. 9), not allembodiments are limited in this respect. According to at least oneembodiment, as few as two temperatures may be used while still providingaccurate temperature calibration and compensation. As few as twotemperatures may be used in situations in which, for example, only thelinear error is compensated during the calibration process by measuringfrequency response at different temperatures. In such situations,temperature measurements and circuit adjustments may be performed at twotemperatures (e.g., Temperatures 1 and 2 in FIG. 9) as previouslydescribed to compensate the linear error. Further temperaturemeasurements may not be needed to compensate the second order errorbecause, for example, the second order error may be known orsubstantially known beforehand (for example, in situations in which thesecond order error does not vary significantly from resonator toresonator and is therefore known from measurements performed on previousresonators). The third order error may simply not be compensated in somesituations if not desired. Thus, accurate temperature compensation maybe provided using as few as two temperature points.

One or more benefits compared to conventional calibration andtemperature compensation technology may be realized by utilizing theaspects described herein. For example, the time involved in calibratingtemperature compensation circuitry may be reduced, and in some instancessignificantly reduced, by utilizing one or more of the aspectsdescribed. As a non-limiting example, compared to measuring thefrequency response of an oscillator at over 1,200 temperatures, asconventionally done, much less time may be involved in using the methodsdescribed herein in which significantly fewer temperatures are analyzed(e.g., ten temperatures or less). Moreover, while conventionalcalibration techniques require a second temperature sweep over theentire operating temperature range, at least some of the aspectsdescribed herein may negate the need for any such confirmationtemperature sweep, thus saving further time and effort. Furthermore,compared to storing calibration values for a large number oftemperatures (e.g., 1,200), as conventionally done, significantly lessor no storage may be needed according to at least some of the aspectsdescribed herein. Additionally, as described previously, at least someof the aspects described herein allow for temperature calibration to beperformed without precise temperatures, thus easing constraints on theprocess. In other words, the calibration may be performed irrespectiveof whether the test temperature is, for example, 33C or 35C. Usingstable test temperatures may be sufficient (e.g., a test temperaturethat remains at 33C during the testing at that temperature).

It should be appreciated that various aspects are described herein.According to one aspect, circuits and methods for calibratingtemperature compensation circuitry of an oscillator by measuring thefrequency of the oscillator at distinct and well controlled temperaturesand adjusting a circuit until the oscillator frequency matches thedesired frequency are provided. In some such situations, the calibrationmay be performed without measuring the oscillator behavior over anentire operating temperature range and without computing best adjustmentsettings for multiple components of a temperature compensation circuit.Thus, aspects of the present invention may be simpler and more robustthan conventional techniques for calibration of temperature compensationcircuitry.

According to some non-limiting embodiments of the above-describedaspect, the frequency error for the temperatures used to adjust thecalibration circuit may be minimal and may not be affected by anysubsequent calibration step. Thus, the adjustment of individualcomponents of a temperature compensation circuit may be independent ofthe adjustment of other components of the circuit.

According to another aspect, a calibration method of an oscillator isprovided for calibrating the oscillator frequency behavior over atemperature range (e.g., an operating temperature range). Thecalibration may method may be designed to avoid any final temperaturesweep conventionally required to ensure accuracy of the calibration. Insome non-limiting embodiments, the calibration method also, oralternatively, does not require a full sweep over the entire temperatureoperating range before adjusting the temperature compensation circuit.According to some non-limiting embodiments, the calibration methodinvolves making circuit adjustments at each of multiple temperaturesteps of the calibration method, rather than measuring the oscillatorfrequency at many temperatures and then making one adjustment. In somenon-limiting embodiments, the calibration method may use temperaturesthat are precise (stable) (i.e. temperature stability of e.g. ±2K,±0.5K, ±0.1K) but not necessarily accurate (i.e., that do notnecessarily equal a specifically targeted temperature value).

According to one aspect, temperature compensation circuitry is providedincluding one or more digital-to-analog converters (DACs). Calibrationof the temperature compensation circuitry may comprise adjusting theDACs by programming them. In some non-limiting embodiments, the DACs arenon-linear, though in some embodiments linear DACs may be used. Thetemperature calibration may be performed without evaluating the DACdigital-to-analog conversion relation prior to setting the DAC. Thecalibration may involve adjusting each DAC until the oscillatorfrequency matches a desired frequency.

According to another aspect, compensation of arbitrary frequencyoscillators may be accomplished using one or more of the techniquesdescribed herein. However, it should be appreciated that the techniquesmay be applied to various types of oscillators, and arbitrary frequencyoscillators represent a non-limiting example.

According to another aspect, temperature calibration techniquesdescribed herein may utilize various temperatures for the calibration.Various scenarios are possible, some non-limiting examples of which arenow described.

According to some embodiments, it may be desirable to apply one or moreof the techniques described herein to resonators whose temperaturedependent frequency shows a strong cubic characteristic, such as AT-cutquartz crystals. According to some such embodiments, it may be desirableto null the temperature sensor as described above around the center ofthe operating temperature range within 20% tolerance of the absoluterange of the temperature range at a first temperature. To address alinear coefficient of the temperature dependent frequency behavior, atemperature between 34° C. and 39° C. may be implemented as a secondtemperature. To address a quadratic component of the temperaturedependent frequency behavior, a temperature between 11° C. and 39° C.(e.g., between 35° C. and 39° C.) may be used as a third temperature. Toaddress a cubic component of the temperature dependent frequencybehavior, a temperature between 39° C. to 85° C. or lower than 11° C.(e.g., between 11° C. and −40° C.) may be used as a fourth temperature.These are non-limiting examples.

According to some embodiments, it may be desirable to apply one or moreof the techniques described herein to resonators whose temperaturedependent frequency shows a strong quadratic characteristic, such asBT-cut crystals, MEMS resonators, and temperature compensated FBARs.According to some such embodiments, it may be desirable to null thetemperature sensor as described above around the center of the operatingtemperature range within 20% tolerance of the absolute range of thetemperature range at a first temperature. To address a linearcoefficient of the temperature dependent frequency behavior, atemperature close to the center of the operating temperature range maybe chosen as the second temperature, e.g., within the range includingthe center of the temperature range ±20% of the absolute range of thetemperature range. To address a quadratic component of the temperaturedependent frequency behavior, a temperature close to the extremes of thetemperature range may be selected as a third temperature, e.g., within30% tolerance of the absolute range of the temperature range. To performa linear re-adjustment step on such types of resonators (i.e., using afourth temperature), the fourth temperature may be chosen in the centerof the third temperature and second temperature within 20% tolerance ofthe absolute temperature range. Alternatively, the fourth temperaturemay be located within ±25% from the extreme temperature with a 40%tolerance of the absolute temperature range. To address a cubiccomponent of the temperature dependent frequency behavior, a temperatureclose to the extremes of the temperature range may be selected as afifth calibration temperature, e.g., within 40% of the absolute range ofthe temperature range. These are non-limiting examples.

According to some embodiments, it may be desirable to apply one or moreof the techniques described herein to oscillators where the lowesttemperature used during calibration is limited. For example, accordingto one embodiment, the techniques described herein may be applied tocalibration of an oscillator when the lowest temperature range ofcalibration is not lower than the center of the specified operatingrange of the oscillator. In some embodiments, the calibration may beapplied when the lowest temperature of the calibration is 10% of thetotal operating temperature range lower than the center temperature ofthe operating range. In some embodiments, the calibration may be appliedwhen the lowest temperature of the calibration is 20% of the totaloperating temperature range lower than the center temperature of theoperating range. In some embodiments, the calibration may be appliedwhen the lowest temperature of the calibration is 30% of the totaloperating range lower than the center temperature of the operatingrange. Alternatives are possible.

Having thus described several aspects of at least one embodiment of thetechnology, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those skilled inthe art. Such alterations, modifications, and improvements are intendedto be within the spirit and scope of the technology. Accordingly, theforegoing description and drawings provide non-limiting examples only.

In addition, while some references have been incorporated herein byreference, it should be appreciated that the present applicationcontrols to the extent the incorporated references are contrary to whatis described herein.

1. A method of calibrating temperature compensation circuitry of anoscillator, the oscillator comprising a mechanical resonator coupled tothe temperature compensation circuitry, the method comprising: setting afirst temperature of the oscillator; adjusting a first component of thetemperature compensation circuitry to set an output frequency of theoscillator to a desired value at the first temperature; setting a secondtemperature of the oscillator; and adjusting a second component of thetemperature compensation circuitry to set the output frequency of theoscillator to the desired value at the second temperature.
 2. The methodof claim 1, wherein the first component and the second component aredigital-to-analog converters (DACs), and wherein setting thosecomponents comprises programming values into those components.
 3. Themethod of claim 2, wherein the DACs are not linear DACS.
 4. The methodof claim 1, further comprising setting a third temperature of theoscillator and adjusting a third component of the temperaturecompensation circuitry to set the output frequency of the oscillator tothe desired value at the third temperature.
 5. The method of claim 4,wherein the method of calibrating the temperature compensation circuitryinvolves measuring the output frequency of the oscillator at fewer thansix temperatures.
 6. The method of claim 5, wherein the method ofcalibrating the temperature compensation circuitry involves measuringthe output frequency of the oscillator at fewer than four temperatures.7. The method of claim 1, wherein the method of calibrating thetemperature compensation circuitry does not involve performing atemperature sweep with the oscillator.
 8. The method of claim 1, whereinthe first and second temperatures are stable but not accurate.
 9. Themethod of claim 1, further comprising setting a third temperature of theoscillator and adjusting a third component of the temperaturecompensation circuitry to set the output frequency of the oscillator tothe desired value at the third temperature, wherein each of the first,second, and third components is a digital-to-analog converter (DAC)configured to independently adjust the output frequency of theoscillator independent of the other two of the DACs.
 10. A temperaturecompensation circuit configured to form part of an oscillator comprisinga mechanical resonator, the temperature compensation circuit comprising:at least first and second adjustable circuit components configured toindependently alter an output frequency of the oscillator.
 11. Thetemperature compensation circuit of claim 10, wherein the at least firstand second adjustable circuit components are digital-to-analogconverters (DACs).
 12. The temperature compensation circuit of claim 10,wherein the at least first and second adjustable circuit componentscomprise a first adjustable circuit component, a second adjustablecircuit component, and a third adjustable circuit component, and whereinthe first adjustable circuit component is configured to control a linearcomponent of a temperature-dependent frequency response of theoscillator, wherein the second adjustable circuit component isconfigured to control a quadratic component of the temperature-dependentfrequency response of the oscillator, and wherein the third adjustablecircuit component is configured to control a cubic component of thetemperature-dependent frequency response of the oscillator.
 13. Thetemperature compensation circuit of claim 12, further comprising aplurality of adders coupled to the first, second, and third adjustablecircuit components.
 14. The temperature compensation circuit of claim13, wherein each of the first, second, and third adjustable circuitcomponents is a digital-to-analog converter (DAC), and wherein thetemperature compensation circuit further comprises a fourth DAC coupledto at least one first adder of the plurality of adders and a fifth DACcoupled to at least one second adder of the plurality of adders.
 15. Thetemperature compensation circuit of claim 13, wherein one adder of theplurality of adders receives an input from a temperature sensor.